<TeXmacs|2.1.1>

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  <doc-data|<doc-title|2021\<#5E74\>\<#6D59\>\<#6C5F\>\<#7701\>\<#9AD8\>\<#8003\>\<#6570\>\<#5B66\>\<#7B2C\>\<#4E03\>\<#9898\>\<#51FD\>\<#6570\>\<#66F2\>\<#7EBF\>\<#7ED8\>\<#5236\>>>

  2021\<#5E74\>\<#6D59\>\<#6C5F\>\<#7701\>\<#9AD8\>\<#8003\>\<#6570\>\<#5B66\>\<#9009\>\<#62E9\>\<#9898\>\<#7B2C\>\<#4E03\>\<#9898\>\<#5982\>\<#4E0B\>\<#6240\>\<#793A\>\<#FF1A\>

  <\framed>
    7. \<#5DF2\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around*|(|x|)>=x<rsup|2>+<frac|1|4>,g<around*|(|x|)>=sin
    x>\<#FF0C\>\<#5219\>\<#56FE\>\<#50CF\>\<#4E3A\>\<#5982\>\<#56FE\>\<#7684\>\<#51FD\>\<#6570\>\<#53EF\>\<#80FD\>\<#662F\>

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    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|y=f<around*|(|x|)>+g<around*|(|x|)>-<frac|1|4>>
      </cell>|<\cell>
        B. <math|y=f<around*|(|x|)>-g<around*|(|x|)>-<frac|1|4>>
      </cell>>|<row|<\cell>
        C. <math|y=f<around*|(|x|)> g<around*|(|x|)>>
      </cell>|<\cell>
        D. <math|y=<frac|g<around*|(|x|)>|f<around*|(|x|)>>>
      </cell>>>>
    </wide-tabular>
  </framed>

  \<#672C\>\<#6587\>\<#5C06\>\<#4ECE\>\<#5982\>\<#4F55\>\<#7ED8\>\<#5236\><math|sin<around*|(|x|)>>\<#5F00\>\<#59CB\>\<#8BB2\>\<#89E3\>\<#5982\>\<#4F55\>\<#7ED8\>\<#5236\>\<#9898\>\<#76EE\>\<#4E2D\>\<#7684\>\<#9009\>\<#9879\>D\<#3002\>

  <section*|\<#63D2\>\<#5165\><name|Gnuplot>\<#4F1A\>\<#8BDD\>>

  \<#672C\>\<#6587\>\<#4F7F\>\<#7528\><name|Gnuplot>\<#6765\>\<#7ED8\>\<#5236\>\<#51FD\>\<#6570\>\<#66F2\>\<#7EBF\>\<#FF0C\>\<#8BF7\>\<#63D0\>\<#524D\>\<#5B89\>\<#88C5\>\<#597D\><name|Gnuplot>\<#8FD9\>\<#4E2A\>\<#8F6F\>\<#4EF6\>\<#FF0C\>\<#5E76\>\<#4FDD\>\<#8BC1\>\<#5728\>\<#58A8\>\<#5E72\>\<#7F16\>\<#8F91\>\<#5668\>\<#4E2D\>\<#53EF\>\<#4EE5\>\<#4F7F\>\<#7528\><name|Gnuplot>\<#4F1A\>\<#8BDD\>\<#3002\>\<#FF08\>\<#63D0\>\<#793A\>\<#FF1A\>Windows\<#5E73\>\<#53F0\>\<#9664\>\<#4E86\>\<#5B89\>\<#88C5\><name|Gnuplot>\<#4E4B\>\<#5916\>\<#FF0C\>\<#8FD8\>\<#9700\>\<#8981\>\<#989D\>\<#5916\>\<#4ECE\>Windows\<#5E94\>\<#7528\>\<#5546\>\<#5E97\>\<#5B89\>\<#88C5\>Python\<#FF0C\>\<#5EFA\>\<#8BAE\>\<#5B89\>\<#88C5\>Python3.8.x\<#FF09\>

  \<#5728\>\<#58A8\>\<#5E72\>\<#7F16\>\<#8F91\>\<#5668\>\<#4E2D\>\<#FF0C\>\<#4F7F\>\<#7528\><menu|Insert|Fold|Executable|Gnuplot>\<#5C31\>\<#53EF\>\<#4EE5\>\<#63D2\>\<#5165\>\<#4E00\>\<#4E2A\><name|Gnuplot>\<#4F1A\>\<#8BDD\>\<#3002\>

  <\session|gnuplot|default>
    <\output>
      gnuplot 5.4 patchlevel 2
    </output>

    <\input>
      gnuplot]\ 
    <|input>
      \;
    </input>
  </session>

  <section*|\<#7ED8\>\<#5236\><math|sin<around*|(|x|)>>>

  <\session|gnuplot|default>
    <\unfolded-io>
      gnuplot]\ 
    <|unfolded-io>
      % -width 0.618par

      plot sin(x)
    <|unfolded-io>
      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    </unfolded-io>

    <\input>
      gnuplot]\ 
    <|input>
      \;
    </input>
  </session>

  \<#4E0D\>\<#505A\>\<#4EFB\>\<#4F55\>\<#914D\>\<#7F6E\>\<#FF0C\>\<#76F4\>\<#63A5\>\<#7ED8\>\<#5236\><math|sin<around*|(|x|)>>\<#FF0C\>\<#9ED8\>\<#8BA4\>\<#7684\>\<#56FE\>\<#50CF\>\<#4E0D\>\<#591F\>\<#53CB\>\<#597D\>\<#3002\>

  <section*|\<#7F8E\>\<#5316\><math|sin<around*|(|x|)>>>

  \<#6211\>\<#4EEC\>\<#6765\>\<#9010\>\<#6B65\>\<#8C03\>\<#6574\>\<#4E00\>\<#4E0B\>\<#3002\>\<#9996\>\<#5148\>\<#5C06\>\<#4E0A\>\<#56FE\>\<#7684\>\<#8FB9\>\<#6846\>\<#6362\>\<#6210\>\<#6211\>\<#4EEC\>\<#719F\>\<#6089\>\<#7684\>\<#5750\>\<#6807\>\<#8F74\>\<#FF1A\>

  <\session|gnuplot|default>
    <\unfolded-io>
      gnuplot]\ 
    <|unfolded-io>
      % -width 0.618par

      <\with|color|red>
        unset border

        set zeroaxis linetype -1 linewidth 2

        set xtics axis

        set ytics axis
      </with>

      plot sin(x)
    <|unfolded-io>
      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    http://gnuplot.info/docs_5.5/loc9713.html
  </footnote>\<#7684\>\<#4F5C\>\<#7528\>\<#662F\>\<#628A\>\<#5916\>\<#9762\>\<#7684\>\<#8FB9\>\<#6846\>\<#53BB\>\<#6389\>\<#FF0C\><verbatim|zeroaxis><\footnote>
    http://gnuplot.info/docs_5.5/loc16801.html
  </footnote>\<#53EF\>\<#7528\>\<#4E8E\>\<#8BBE\>\<#7F6E\>\<#4E24\>\<#4E2A\>\<#5750\>\<#6807\>\<#8F74\>\<#90FD\>\<#7ECF\>\<#8FC7\>\<#539F\>\<#70B9\>\<#3002\>

  \<#901A\>\<#8FC7\>\<#4E0A\>\<#9762\>\<#56DB\>\<#884C\>\<#914D\>\<#7F6E\>\<#FF0C\>\<#6211\>\<#4EEC\>\<#5F97\>\<#5230\>\<#4E00\>\<#4E2A\>\<#5728\>\<#4E2D\>\<#5B66\>\<#6559\>\<#80B2\>\<#4E2D\>\<#7ECF\>\<#5E38\>\<#4F7F\>\<#7528\>\<#5230\>\<#7684\>\<#51FD\>\<#6570\>\<#66F2\>\<#7EBF\>\<#56FE\>\<#50CF\>\<#3002\>

  \<#53EF\>\<#4EE5\>\<#518D\>\<#505A\>\<#4E00\>\<#4E9B\>\<#8C03\>\<#6574\>\<#FF0C\>\<#8BA9\>\<#8FD9\>\<#4E2A\>\<#56FE\>\<#50CF\>\<#66F4\>\<#52A0\>\<#7F8E\>\<#89C2\>\<#4E00\>\<#4E9B\>\<#FF1A\>

  <\session|gnuplot|default>
    <\folded-io>
      gnuplot]\ 
    <|folded-io>
      % -width 0.618par

      unset border

      set zeroaxis linetype -1 linewidth 2

      set xtics axis

      set ytics axis

      \;

      <\with|color|red>
        set xtics pi

        set ytics 1

        set arrow from 0,0 to 10,0

        set arrow from 0,0 to 0,1.5
      </with>

      \;

      plot <with|color|red|[-10:10][-1.5:1.5]> sin(x)
      <with|color|red|linecolor rgb "black">
    <|folded-io>
      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    </folded-io>

    <\input>
      gnuplot]\ 
    <|input>
      \;
    </input>
  </session>

  \<#63A5\>\<#4E0B\>\<#6765\>\<#65B0\>\<#589E\>\<#7684\>\<#56DB\>\<#884C\>\<#FF0C\>\<#6211\>\<#4EEC\>\<#914D\>\<#7F6E\>\<#4E86\><math|x>\<#8F74\>\<#7684\>\<#523B\>\<#5EA6\>\<#5355\>\<#4F4D\>\<#662F\><math|\<pi\>>\<#FF0C\><math|y>\<#8F74\>\<#7684\>\<#523B\>\<#5EA6\>\<#5355\>\<#4F4D\>\<#662F\>1\<#FF0C\>\<#7136\>\<#540E\>\<#7ED8\>\<#5236\>\<#4E86\>\<#4E24\>\<#4E2A\>\<#7BAD\>\<#5934\>\<#3002\>\<#5728\>\<#6700\>\<#540E\>\<#7684\>plot\<#547D\>\<#4EE4\>\<#4E2D\>\<#FF0C\>\<#8BBE\>\<#7F6E\>\<#4E86\>\<#5B9A\>\<#4E49\>\<#57DF\>\<#4E3A\><math|<around*|[|-10:10|]>>\<#FF0C\>\<#503C\>\<#57DF\>\<#4E3A\><math|<around*|[|-1.5:1.5|]>>\<#FF0C\>\<#6700\>\<#540E\>\<#628A\>\<#66F2\>\<#7EBF\>\<#989C\>\<#8272\>\<#8C03\>\<#6574\>\<#6210\>\<#4E86\>\<#9ED1\>\<#8272\>\<#3002\>

  \<#901A\>\<#8FC7\>\<#4EE5\>\<#4E0A\>\<#914D\>\<#7F6E\>\<#FF0C\>\<#6211\>\<#4EEC\>\<#5F97\>\<#5230\>\<#4E00\>\<#4E2A\>\<#5728\>\<#4E2D\>\<#5B66\>\<#6559\>\<#80B2\>\<#4E2D\>\<#7ECF\>\<#5E38\>\<#4F7F\>\<#7528\>\<#7684\>\<#51FD\>\<#6570\>\<#66F2\>\<#7EBF\>\<#56FE\>\<#50CF\>\<#3002\>

  <section*|\<#7ED8\>\<#5236\>\<#9009\>\<#9879\>D>

  \<#6211\>\<#4EEC\>\<#9009\>\<#4E2D\>\<#4E0A\>\<#4E00\>\<#4E2A\>\<#5C0F\>\<#8282\>\<#4E2D\>\<#7684\>\<#4EE3\>\<#7801\>\<#7247\>\<#6BB5\>\<#FF0C\>\<#4F7F\>\<#7528\>\<#53F3\>\<#952E\>\<#83DC\>\<#5355\>\<#590D\>\<#5236\>\<#FF0C\>\<#7136\>\<#540E\>\<#4F7F\>\<#7528\>\<#53F3\>\<#952E\>\<#83DC\>\<#5355\>\<#7C98\>\<#8D34\>\<#5230\>\<#4E0B\>\<#9762\>\<#7684\>\<#4F1A\>\<#8BDD\>\<#4E2D\>\<#3002\>\<#4FEE\>\<#6539\>plot\<#547D\>\<#4EE4\>\<#91CC\>\<#9762\>\<#7684\>\<#51FD\>\<#6570\>\<#FF0C\>\<#5C31\>\<#53EF\>\<#4EE5\>\<#7ED8\>\<#5236\>\<#9009\>\<#9879\>D\<#7684\>\<#66F2\>\<#7EBF\>\<#FF08\>\<#5728\>\<#8FD9\>\<#4E2A\>\<#4F8B\>\<#5B50\>\<#4E2D\>\<#FF0C\>\<#6211\>\<#4EEC\>\<#7A0D\>\<#7A0D\>\<#8C03\>\<#6574\>\<#4E00\>\<#4E0B\>\<#523B\>\<#5EA6\>\<#3001\>\<#5B9A\>\<#4E49\>\<#57DF\>\<#3001\>\<#503C\>\<#57DF\>\<#4EE5\>\<#66F4\>\<#52A0\>\<#6E05\>\<#695A\>\<#5730\>\<#5C55\>\<#793A\>\<#66F2\>\<#7EBF\>\<#7684\>\<#6027\>\<#8D28\>\<#FF09\>\<#FF1A\>

  <\session|gnuplot|default>
    <\unfolded-io>
      gnuplot]\ 
    <|unfolded-io>
      % -width 0.8par

      unset border

      set zeroaxis linetype -1 linewidth 2

      set xtics axis

      set ytics axis

      \;

      set xtics pi

      set ytics 0.5

      set arrow from 0,0 to 15,0

      set arrow from 0,0 to 0,1.2

      \;

      plot [-15:15][-1.2:1.2] <with|color|red|(sin(x)/(x*x+1/4)) \\>

      linecolor rgb "red" <with|color|red|linewidth 1.5>
    <|unfolded-io>
      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    </unfolded-io>

    <\input>
      gnuplot]\ 
    <|input>
      \;
    </input>
  </session>

  \<#4E5F\>\<#53EF\>\<#4EE5\>\<#5728\>\<#540C\>\<#4E00\>\<#4E2A\>\<#6BB5\>\<#843D\>\<#91CC\>\<#9762\>\<#7ED8\>\<#5236\>\<#4E24\>\<#4E2A\>\<#66F2\>\<#7EBF\>\<#FF0C\>\<#5982\>\<#4E0B\>\<#6240\>\<#793A\>\<#FF1A\>

  <\session|gnuplot|default>
    <\unfolded-io>
      gnuplot]\ 
    <|unfolded-io>
      % -width 0.8par

      unset border

      set zeroaxis linetype -1 linewidth 2

      set xtics axis

      set ytics axis

      \;

      set xtics pi

      set ytics 0.5

      set arrow from 0,0 to 15,0

      set arrow from 0,0 to 0,1.2

      \;

      plot [-15:15][-1.2:1.2] \\

      (sin(x)/(x*x+1/4)) linecolor rgb "red" linewidth 1.5<with|color|red|,>
      \\

      <with|color|red|sin(x) linecolor rgb "blue">

      \;
    <|unfolded-io>
      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      gnuplot]\ 
    <|input>
      \;
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  </session>

  \;

  \;

  \;
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